MATLAB: How to define the Conditional probability density function from a n-by-2 matrix

conditional pdfconditional probability

Dear all,

I am currently trying to define the probability density function P(X/Y<y).

I indeed have an n-by-2 matrix where column 1 gives values of X and column 2 gives matrix of Y. They are correlated (coef=0.5).

How can I define the conditional pdf P(X<x/Y<y) from this matrix ?

Thank you for your help!

Best

Laurène

Best Answer

Maybe start with 'ksdensity' to estimate the joint pdf of x & y from your observed x,y pairs. Once you have a good numerical estimate of the joint density at each (x,y) pair, you should be able to estimate whatever you want from that.

It isn't entirely clear what you want to compute, though, because "conditional pdf P(X<x/Y<y)" looks like a conditional CDF instead of PDF. It might help to give a small numerical example to show what number you would like to get.

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MATLAB: How to go about finding the standard normal probability based on the z-score

doc normcdf
doc normpdf

When you know what you want but not sure the name, try something like

>> lookfor normal
realmin                        - Smallest positive normalized floating point number.
randn                          - Normally distributed pseudorandom numbers.
sprandn                        - Sparse normally distributed random matrix.
surfnorm                       - Surface normals.
isonormals                     - Isosurface normals.
cde                            - cd elliptic function with normalized complex argument.
sne                            - sn elliptic function with normalized complex argument.
addfreqcsmenu                  - Add a cs menu to switch between linear and normalized frequency
convertfrequnits               - converts between Normalized, Hz, kHz, etc
histfit                        - Histogram with superimposed fitted normal density.
jbtest                         - Jarque-Bera hypothesis test of composite normality.
lhsnorm                        - Generate a latin hypercube sample with a normal distribution
logncdf                        - Lognormal cumulative distribution function (cdf).
lognfit                        - Parameter estimates and confidence intervals for lognormal data.
logninv                        - Inverse of the lognormal cumulative distribution function (cdf).
lognlike                       - Negative log-likelihood for the lognormal distribution.
lognpdf                        - Lognormal probability density function (pdf).
lognrnd                        - Random arrays from the lognormal distribution.
lognstat                       - Mean and variance for the lognormal distribution.
mvncdf                         - Multivariate normal cumulative distribution function (cdf).
mvnpdf                         - Multivariate normal probability density function (pdf).
mvnrnd                         - Random vectors from the multivariate normal distribution.
normcdf                        - Normal cumulative distribution function (cdf).
normfit                        - Parameter estimates and confidence intervals for normal data.
norminv                        - Inverse of the normal cumulative distribution function (cdf).
normlike                       - Negative log-likelihood for the normal distribution.
normpdf                        - Normal probability density function (pdf).
normplot                       - Displays a normal probability plot.
normrnd                        - Random arrays from the normal distribution.
normspec                       - Plots normal density between specification limits.
normstat                       - Mean and variance for the normal distribution.
logn3fit                       - Fit a 3-param lognormal dist'n using cumulative probabilities.
wgtnormfit                     - Fitting example for a weighted normal distribution.
wgtnormfit2                    - Fitting example for a weighted normal distribution (log(sigma) parameterization).
>>

Judicious search terms help but seeing the list of things related to "normal" lets you find the two functions of interest (plus a lot more depending upon which toolboxes are available, maybe) that might be of use/interest...

MATLAB: How create joint distribution of two dependent variables

I don't think your two questions are equivalent.

If you have the two marginal pdfs and the correlation, there are lots of ways to define the joint distribution--it is not uniquely determined by the marginals and correlation, except in the special case of the bivariate normal. So, you need to choose one of the possible joint distributions depending on your situation. For more information, read about "copulas".

On the other hand, if you have the joint distribution, you can compute everything from it. For example, you can integrate it across one variable to get the marginal distribution for the other variable. Similarly, you can compute the correlation. So, the joint distribution does uniquely determine everything else. Just not vice versa.

Best Answer

Related Solutions

MATLAB: How to go about finding the standard normal probability based on the z-score

MATLAB: How create joint distribution of two dependent variables

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